We study the convergence of the derivative expansion
in HAL QCD method from the finite volume analysis.
Employing the (2+1)-flavor lattice QCD data obtained at nearly physical light quark masses
$(m_\pi, m_K) \simeq (146, 525)$ MeV and the physical charm quark mass,
we study two representative systems, $\Omega\Omega$ and $\Omega_{ccc}\Omega_{ccc}$ in the $^1S_0$ channel,
where both systems were found to have a shallow bound state in our previous studies.
The HAL QCD potentials are determined at the leading-order in the derivative expansion,
from which finite-volume eigenmodes are obtained.
Utilizing the eigenmode projection,
we find that the correlation functions are dominated by
the ground state (first excited state) in the case of $\Omega\Omega$ ($\Omega_{ccc}\Omega_{ccc}$).
In both $\Omega\Omega$ and $\Omega_{ccc}\Omega_{ccc}$,
the spectra obtained from eigenmode-projected temporal correlators
are found to be consistent with those from the HAL QCD potential for both
the ground and first excited state.
These results show that the derivative expansion is well converged in these systems,
and also provide a first explicit evidence that
the HAL QCD method enables us to reliably extract
the binding energy of the ground state
even from the correlator dominated by excited scattering states.